Well, if I know what it is I can dismiss it. If I don't know what it is and I think it's me, I might entertain it. Over time I might give the motor control over to the beast.
Actually, I did that several years ago.
As far as this:
But does it matter whether it is me or the AV who thinks a drink is tasty or wishes I were capable of 'normal drinking', as long as I am not going to violate the BP?
Per AVRT (important preface), any thought, in words or images, that suggests (even remotely) the use of alcohol now or in the future is AV....so, according to AVRT, it's always AV, never you. The reason it is outlined like that is to make it simple. Continually questioning "is it?" or "Isn't it?" puts you in a position for beast take-over.
Weird analogy, but you know how you check out some leftovers in the fridge and stand there for a min like...."hmmmm, I wonder if these are still good...." It's not even worth knowing the answer because finding the answer would involve unnecessary risk. Even a remote possibility and it gets tossed. It's just easier that way.